Handing Wang

Two_Arch2: An Improved Two-Archive Algorithm for Many-Objective Optimization

Many-objective optimization problems (ManyOPs) refer, usually, to those multiobjective problems (MOPs) with more than three objectives. Their large numbers of objectives pose challenges to multiobjective evolutionary algorithms (MOEAs) in terms of convergence, diversity, and complexity. Most existing MOEAs can only perform well in one of those three aspects. In view of this, we aim to design a more balanced MOEA on ManyOPs in all three aspects at the same time. Among the existing MOEAs, the two-archive algorithm (Two_Arch) is a low-complexity algorithm with two archives focusing on convergence and diversity separately. Inspired by the idea of Two_Arch, we propose a significantly improved two-archive algorithm (i.e., Two_Arch2) for ManyOPs in this paper. In our Two_Arch2, we assign different selection principles (indicator-based and Pareto-based) to the two archives. In addition, we design a new Lp-norm-based (p <; 1) diversity maintenance scheme for ManyOPs in Two_Arch2. In order to evaluate the performance of Two_Arch2 on ManyOPs, we have compared it with several MOEAs on a wide range of benchmark problems with different numbers of objectives. The experimental results show that Two_Arch2 can cope with ManyOPs (up to 20 objectives) with satisfactory convergence, diversity, and complexity.

Corner Sort for Pareto-Based Many-Objective Optimization

Nondominated sorting plays an important role in Pareto-based multiobjective evolutionary algorithms (MOEAs). When faced with many-objective optimization problems multiobjective optimization problems (MOPs) with more than three objectives, the number of comparisons needed in nondominated sorting becomes very large. In view of this, a new corner sort is proposed in this paper. Corner sort first adopts a fast and simple method to obtain a nondominated solution from the corner solutions, and then uses the nondominated solution to ignore the solutions dominated by it to save comparisons. Obtaining the nondominated solutions requires much fewer objective comparisons in corner sort. In order to evaluate its performance, several state-of-the-art nondominated sorts are compared with our corner sort on three kinds of artificial solution sets of MOPs and the solution sets generated from MOEAs on benchmark problems. On one hand, the experiments on artificial solution sets show the performance on the solution sets with different distributions. On the other hand, the experiments on the solution sets generated from MOEAs show the influence that different sorts bring to MOEAs. The results show that corner sort performs well, especially on many-objective optimization problems. Corner sort uses fewer comparisons than others.

A co-evolutionary multi-objective optimization algorithm based on direction vectors

Most real world multi-objective problems (MOPs) have a complicated solution space. Facing such problems, a direction vectors based co-evolutionary multi-objective optimization algorithm (DVCMOA) that introduces the decomposition idea from MOEA/D to co-evolutionary algorithms is proposed in this paper. It is novel in the sense that DVCMOA applies the concept of direction vectors to co-evolutionary algorithms. DVCMOA first divides the entire population into several subpopulations on the basis of the initial direction vectors in the objective space. Then, it solves MOPs through the co-evolutionary interaction among the subpopulations in which individuals are classified according to their direction vectors. Finally, it explores the less developed regions to maintain the relatively uniform distribution of the solution space. In this way, DVCMOA has advantages in convergence, diversity and uniform distribution of the non-dominated solution set, which are explained through comparison with other state-of-the-art multi-objective optimization evolutionary algorithms (MOEAs) in this paper. DVCMOA is shown to be effective on 6 multi-objective 0-1 knapsack problems.

Objective reduction based on nonlinear correlation information entropy

It is hard to obtain the entire solution set of a many-objective optimization problem (MaOP) by multi-objective evolutionary algorithms (MOEAs) because of the difficulties brought by the large number of objectives. However, the redundancy of objectives exists in some problems with correlated objectives (linearly or nonlinearly). Objective reduction can be used to decrease the difficulties of some MaOPs. In this paper, we propose a novel objective reduction approach based on nonlinear correlation information entropy (NCIE). It uses the NCIE matrix to measure the linear and nonlinear correlation between objectives and a simple method to select the most conflicting objectives during the execution of MOEAs. We embed our approach into both Pareto-based and indicator-based MOEAs to analyze the impact of our reduction method on the performance of these algorithms. The results show that our approach significantly improves the performance of Pareto-based MOEAs on both reducible and irreducible MaOPs, but does not much help the performance of indicator-based MOEAs.

Data-Driven Surrogate-Assisted Multiobjective Evolutionary Optimization of a Trauma System

Most existing work on evolutionary optimization assumes that there are analytic functions for evaluating the objectives and constraints. In the real world, however, the objective or constraint values of many optimization problems can be evaluated solely based on data and solving such optimization problems is often known as data-driven optimization. In this paper, we divide data-driven optimization problems into two categories, i.e., offline and online data-driven optimization, and discuss the main challenges involved therein. An evolutionary algorithm is then presented to optimize the design of a trauma system, which is a typical offline data-driven multiobjective optimization problem, where the objectives and constraints can be evaluated using incidents only. As each single function evaluation involves a large amount of patient data, we develop a multifidelity surrogate-management strategy to reduce the computation time of the evolutionary optimization. The main idea is to adaptively tune the approximation fidelity by clustering the original data into different numbers of clusters and a regression model is constructed to estimate the required minimum fidelity. Experimental results show that the proposed algorithm is able to save up to 90% of computation time without much sacrifice of the solution quality.

Committee-Based Active Learning for Surrogate-Assisted Particle Swarm Optimization of Expensive Problems

Function evaluations (FEs) of many real-world optimization problems are time or resource consuming, posing a serious challenge to the application of evolutionary algorithms (EAs) to solve these problems. To address this challenge, the research on surrogate-assisted EAs has attracted increasing attention from both academia and industry over the past decades. However, most existing surrogate-assisted EAs (SAEAs) either still require thousands of expensive FEs to obtain acceptable solutions, or are only applied to very low-dimensional problems. In this paper, a novel surrogate-assisted particle swarm optimization (PSO) inspired from committee-based active learning (CAL) is proposed. In the proposed algorithm, a global model management strategy inspired from CAL is developed, which searches for the best and most uncertain solutions according to a surrogate ensemble using a PSO algorithm and evaluates these solutions using the expensive objective function. In addition, a local surrogate model is built around the best solution obtained so far. Then, a PSO algorithm searches on the local surrogate to find its optimum and evaluates it. The evolutionary search using the global model management strategy switches to the local search once no further improvement can be observed, and vice versa. This iterative search process continues until the computational budget is exhausted. Experimental results comparing the proposed algorithm with a few state-of-the-art SAEAs on both benchmark problems up to 30 decision variables as well as an airfoil design problem demonstrate that the proposed algorithm is able to achieve better or competitive solutions with a limited budget of hundreds of exact FEs.

Access to specialist care: Optimizing the geographic configuration of trauma systems.

BACKGROUND The optimal geographic configuration of health care systems is key to maximizing accessibility while promoting the efficient use of resources. This article reports the use of a novel approach to inform the optimal configuration of a national trauma system. METHODS This is a prospective cohort study of all trauma patients, 15 years and older, attended to by the Scottish Ambulance Service, between July 1, 2013, and June 30, 2014. Patients underwent notional triage to one of three levels of care (major trauma center [MTC], trauma unit, or local emergency hospital). We used geographic information systems software to calculate access times, by road and air, from all incident locations to all candidate hospitals. We then modeled the performance of all mathematically possible network configurations and used multiobjective optimization to determine geospatially optimized configurations. RESULTS A total of 80,391 casualties were included. A network with only high- or moderate-volume MTCs (admitting at least 650 or 400 severely injured patients per year, respectively) would be optimally configured with a single MTC. A network accepting lower-volume MTCs (at least 240 severely injured patients per year) would be optimally configured with two MTCs. Both configurations would necessitate an increase in the number of helicopter retrievals. CONCLUSION This study has shown that a novel combination of notional triage, network analysis, and mathematical optimization can be used to inform the planning of a national clinical network. Scotland’s trauma system could be optimized with one or two MTCs. LEVEL OF EVIDENCE Care management study, level IV.

A memetic optimization strategy based on dimension reduction in decision space

There can be a complicated mapping relation between decision variables and objective functions in multi-objective optimization problems (MOPs). It is uncommon that decision variables influence objective functions equally. Decision variables act differently in different objective functions. Hence, often, the mapping relation is unbalanced, which causes some redundancy during the search in a decision space. In response to this scenario, we propose a novel memetic (multi-objective) optimization strategy based on dimension reduction in decision space (DRMOS). DRMOS firstly analyzes the mapping relation between decision variables and objective functions. Then, it reduces the dimension of the search space by dividing the decision space into several subspaces according to the obtained relation. Finally, it improves the population by the memetic local search strategies in these decision subspaces separately. Further, DRMOS has good portability to other multi-objective evolutionary algorithms (MOEAs); that is, it is easily compatible with existing MOEAs. In order to evaluate its performance, we embed DRMOS in several state of the art MOEAs to facilitate our experiments. The results show that DRMOS has the advantage in terms of convergence speed, diversity maintenance, and portability when solving MOPs with an unbalanced mapping relation between decision variables and objective functions.

Optimizing trauma system design: The GEOS (Geospatial Evaluation of Systems of Trauma Care) approach

BACKGROUND Trauma systems have been shown to reduce death and disability from injury but must be appropriately configured. A systematic approach to trauma system design can help maximize geospatial effectiveness and reassure stakeholders that the best configuration has been chosen. METHODS This article describes the GEOS [Geospatial Evaluation of Systems of Trauma Care] methodology, a mathematical modeling of a population-based data set, which aims to derive geospatially optimized trauma system configurations for a geographically defined setting. GEOS considers a region’s spatial injury profile and the available resources and uses a combination of travel time analysis and multiobjective optimization. The methodology is described in general and with regard to its application to our case study of Scotland. RESULTS The primary outcome will be trauma system configuration. CONCLUSION GEOS will contribute to the design of a trauma system for Scotland. The methodology is flexible and inherently transferable to other settings and could also be used to provide assurance that the configuration of existing trauma systems is fit for purpose.

Regularity Model for Noisy Multiobjective Optimization

Regularity models have been used in dealing with noise-free multiobjective optimization problems. This paper studies the behavior of a regularity model in noisy environments and argues that it is very suitable for noisy multiobjective optimization. We propose to embed the regularity model in an existing multiobjective evolutionary algorithm for tackling noises. The proposed algorithm works well in terms of both convergence and diversity. In our experimental studies, we have compared several state-of-the-art of algorithms with our proposed algorithm on benchmark problems with different levels of noises. The experimental results showed the effectiveness of the regularity model on noisy problems, but a degenerated performance on some noisy-free problems.